# ---
# title: 810. Chalkboard XOR Game
# id: problem810
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Math
# link: <https://leetcode.com/problems/chalkboard-xor-game/description/>
# hidden: true
# ---
# 
# We are given non-negative integers nums[i] which are written on a chalkboard.
# Alice and Bob take turns erasing exactly one number from the chalkboard, with
# Alice starting first.  If erasing a number causes the bitwise XOR of all the
# elements of the chalkboard to become 0, then that player loses.  (Also, we'll
# say the bitwise XOR of one element is that element itself, and the bitwise XOR
# of no elements is 0.)
# 
# Also, if any player starts their turn with the bitwise XOR of all the elements
# of the chalkboard equal to 0, then that player wins.
# 
# Return True if and only if Alice wins the game, assuming both players play
# optimally.
# 
#     
#     
#     **Example:**
#     Input: nums = [1, 1, 2]
#     Output: false
#     Explanation: 
#     Alice has two choices: erase 1 or erase 2. 
#     If she erases 1, the nums array becomes [1, 2]. The bitwise XOR of all the elements of the chalkboard is 1 XOR 2 = 3. Now Bob can remove any element he wants, because Alice will be the one to erase the last element and she will lose. 
#     If Alice erases 2 first, now nums becomes [1, 1]. The bitwise XOR of all the elements of the chalkboard is 1 XOR 1 = 0. Alice will lose.
#     
#     
# 
# **Notes:**
# 
#   * `1 <= N <= 1000`. 
#   * `0 <= nums[i] <= 2^16`.
# 
# 
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
